We observed that under \(I>0\) , i.e. when the asymptotic fixation probability is null, it is always possible to see decreasing fixation functions (D0) under these games. Otherwise, under \(I<0\) , i.e. when the mutant strategy fixates finitely in the asymptotic limit, the fixation of hawks under the Hawk-Dove game represented the only one of those game orderings which could have strictly decreasing functions for some choices of the payoff matrix. In section REF , we propose an explanation for why fixation function shapes beyond the decreasing one have not been referred to in most of the previous literature, with the exception of [1]}. This is so despite the fact they are always observed under some of these game orderings, such as the one which represents the fixation of mutant doves under the Hawk-Dove game.
